Question: Alanna went for a run. She ran $d$ kilometers at an average speed of $v$ kilometers per hour, and then walked to cool down for $0.25$ hours. The total duration of the trip was $t$ hours. Write an equation that relates $d$, $v$, and $t$.
Explanation: Let's find the time Alanna spent running, before the cool-down part. Then we can add $0.25$ hours to represent the total duration, $t$. Alanna ran $d$ kilometers at an average speed of $v$ kilometers per hour, so it took her $\dfrac dv$ hours: $\begin{aligned} &\phantom{=}\dfrac{\left(d\,\text{kilometers}\right)}{\left(v\,\dfrac{\text{kilometers}}{\text{hour}}\right)} \\\\ &=\dfrac dv\,\cancel\text{kilometers}\cdot\dfrac{\text{hours}}{\cancel\text{kilometer}} \\\\ &=\dfrac dv\,\text{hours} \end{aligned}$ Now we can add $0.25$ to get the total duration $t$ : $\dfrac dv+0.25=t$